Primary concentrator with adjusted etendue combined with secondaries associated to multiple receivers and with convection reduction

ABSTRACT

The present invention relates to primary and secondary concentrators of solar radiation. New primary concentrators of adjusted etendue combined with secondary concentrators are presented, for single of multiple receivers, capable of attaining the maximum possible concentration. The present invention also refers to devices which reduce the thermal losses by convection of the receivers.

FIELD OF THE INVENTION

The present invention relates to primary and secondary solar radiation concentrators. The invention relates to new primary etendue adjusted concentrators, combined with secondary ones, for simple or multiple receivers, able to reach the highest concentration value possible. The present invention also relates to devices to reduce thermal losses due to convection at the receivers.

BACKGROUND OF THE INVENTION

Large-scale solar power plants can produce large quantities of electric power. This means that large quantities of sunlight must be collected.

Some of these plants may simply collect sunlight without concentrating it, as in the case of using flat photovoltaic panels exposed to the sunlight. However, when using high-efficiency solar cells or thermodynamic cycles, some degree of concentration is needed to increase efficiency and, therefore, typically also some tracking of the sun.

Sunlight is concentrated using optics. There are cases in which a large number of small optics are placed side by side, each one of them with its own receiver. That is the of, say, a set of parabolic primaries with solar cells at the foci, or adding kaleidoscopes to improve irradiance uniformity on the cell [Daniel Feuermann and Jeffrey M. Gordon, Solar Fiber-optic mini-dishes: a new approach to the efficient collection of sunlight, Solar Energy Vol. 65, No. 3, pp. 159-170, 1999]. In other cases, a smaller number of larger receivers is used, but then large optics are needed. The problem with large optics is that they are hard to assemble and move to track the sun. One possible way around this problem is to replace the large optic by a large number of small optics that mimic its behaviour. One example of this process is found in the tower power plants which have a large number of small mirrors called heliostats that reflect the light to a large receiver. In this case, instead of a large parabolic primary, these plants have a “Fresnel” primary composed of many small mirrors. [J. I. Ortega, J. I. Burgaleta, F. M. Tellez, Central Receiver System (CRS) Solar Power Plant using Molten Salts as Heat Transfer Fluid, Proceedings 13th International Symposium on Solar Power and Chemical Energy Technologies ISBN 84-7834-519-1, Edit. M. Romero, D. Martinez, V. Ruiz, M. Silva, M. Brown, M. Snachez, M. Romero, Methodology for generation of heliostat field layout in central receiver system based on yearly normalized energy surfaces, Solar Energy 80, pp 861-874, 2006].

A further possibility is to have trough receivers onto which light is concentrated using trough optics. Also in this case parabolic primaries may be used [E. Rojas, A. Fernandez, E. Zarza, Theoretical evaluation of parabolic trough designs for industrial applications, Proceedings 13th International Symposium on Solar Power and Chemical Energy Technologies ISBN 84-7834-519-1, Edit. M. Romero, D. Martinez, V. Ruiz, M. Silva, M. Brown], or alternatively “Fresnel” primaries composed of long linear heliostats running in the direction of the receiver [Patente U.S. Pat. No. 4,131,336: Miller et al., Primary reflector for solar energy collection system, 1978, Solar thermal power plants, Renewable Energy World 06/2003 pp. 109-113]. The heliostats may track the sun keeping the receiver illuminated by concentrated sunlight. However, the heliostats shade each other, especially those further away from the receiver, and the light that is shaded is lost. The concentration of these primaries may be increased by secondary optics, such as the TERC secondaries [J. M. Gordon and Harald Ries, Tailored edge-ray concentrators as ideal second stages for Fresnel reflectors, Applied Optics, Vol. 32, No. 13, pp. 2243-2251, 1993]. These concentrators will, however, only approach the theoretical maximum concentration in the limit case of a primary composed of infinitesimal heliostats, a severe practical limitation.

In the prior art, an improvement over a simple “Fresnel” primary is to intersect two heliostat fields in an arrangement know as CLFR (Compact Linear Fresnel Reflector) [David R. Mills and Graham L. Morrison, Compact linear Fresnel reflector solar thermal power plants, Solar Energy Vol. 68, No. 3, pp. 263-283, 2000; U.S. Pat. No. 5,899,199: David Mills, Solar Energy Collector system, 1999, U.S. Pat. No. 6,131,565: David Mills, Solar Energy Collector system, 2000]. In this arrangement, instead of a single receiver there are several receivers. The heliostats are all the same size and those closer to a first receiver redirect the light to it. Those more spaced apart, alternatively redirect the light to the first receiver and to a second receiver. This creates a W shaped heliostat field in the areas more spaced apart from the receivers where the odd heliostats reflect light to one receiver, while the even heliostats reflect light to the other receiver. This approach, however, still does not adjust the etendue of the incoming radiation with that reflected to the receivers and, therefore, there will always be either some shading of light or areas of the heliostat field not fully illuminated when seen from the receivers.

This is a fundamental limitation of these optics and is independent of the size or shape of the heliostats. The concentrations attained by these optics are much lower than the theoretical limit.

To solve the etendue mismatch problem between the etendue of the light received by the primary and the etendue the primary should ideally redirect towards the receivers, new primaries are needed.

The present invention discloses two different ways of improving the primary: changing its overall shape and changing the size and shape of its heliostats. To increase concentration and approach the theoretical limit, the new primaries must be combined with new secondary optics.

When changing the overall shape of the primary, the heliostats are placed on a wave shaped trough surface and the size and shape of the heliostats is a function of the position in the heliostat field. The heliostats may also be flat, in which case the smaller the heliostats, the higher the concentration the primary can provide.

The size and shape of the heliostats may be adjusted in order to increase concentration, which can further be augmented with the use of a secondary. The heliostats constitute a discontinuous primary and, in order to design a continuous secondary, a continuous primary is developed. The heliostats are inter connected by flow lines resulting in a continuous primary (broken line) for which a continuous secondary can be designed. The portions of primary along flow lines can then be removed, leaving the initial heliostats present at the start of the procedure. In this concept the primary is conceived (for the purpose of secondary design) has a continuous but broken mirror, i.e. in steps, portions of which follow flow lines and other portions are transverse to those flow lines [Pablo Benitez, Juan Carlos Minano, Maikel Hernandez, On the analysis of microstructured surfaces, SPIE Proceedings, Vol. 5529, Nonimaging Optics and Efficient Illumination Systems, pp. 186-197, 2004]. This type of design is common in Fresnel Lens design, which can also be combined with secondaries to increase their concentration [M. Collares Pereira, A. Rabl and R. Winston, Lens-mirror combination with maximal concentration, Applied Optics, Vol. 16, No. 10, pp. 2677-2683, 1977, M. Collares Pereira, High temperature solar collector with optimal concentration: non-focusing Fresnel lens with a secondary concentrator, Solar Energy, Vol. 23, pp. 40-9420, 1979, Ralf Leutz, Akio Suzuki, Atsushi Akisawa and Takao Kashiwagi, Design of a nonimaging lens for solar concentrators, Solar Energy, Vol. 65, No. 6, pp. 379-387, 1999]. Other more elaborated types of stepped optics are also possible [Julio Chaves, Manuel Collares-Pereira, Ultra flat ideal concentrators of high concentration, Solar Energy Vol. 69, No. 4, pp. 269-281, 2000, Julio Chaves and Manuel Collares-Pereira, Ideal concentrators with gaps, Applied Optics, Vol. 41, No. 7, pp, 1267-1276, 2002 Julio Chaves, Introduction to Nonimaging Optics, CRC Press, Taylor and Francis Group, 2008]. Continuous secondaries may also be directly designed from discontinuous primaries (a set of heliostats) in which case joining the primary heliostats by flow lines is not required. In this version the heliostats may be on the wave shaped surface or on a flat one. The secondary concentrators conceived for these new primaries are continuous, from portion to portion, in accordance with the piece wise nature of the primary.

In the case of a single receiver, the concentrators thus obtained compare favourably to traditional combinations of Fresnel reflectors and secondaries, increasing the concentration on the receiver close to the theoretical maximum, even for primaries composed of large size heliostats. In the case of multiple receivers, these new concentrators also compare favourably to CLFRs, once again achieving concentrations on the receivers close to the theoretical maximum, while having lower losses.

The secondary mirrors typically touch the receiver and a method for preventing/solve such problem is also disclosed.

The invention further includes devices for reducing convection losses in the receiver. These include specially shaped mirrors and transparent covers.

SUMMARY OF THE INVENTION

The present invention relates to an optical system with primary concentrator of the Fresnel type and secondary concentrator adjacent to the receiver, the secondary-receiver set being above the primary and characterized by the primary concentrator containing a stepped flow-line optics which shape verifies the fact that it reflects a set of edge rays tangent to the receiver and the other set of edge rays into the direction of the secondary concentrator which has a shape that (in turn) reflects those edge rays tangent to the receiver producing theoretically there maximum concentration and in which the secondary concentrator is truncated.

In one embodiment, the optical system is characterized by the receiver having a convex face and also a planar one in which the secondary receiver touches only in one point and in which the planar face may be substituted with a concave one resulting in a secondary that does not touch the receiver.

In another embodiment, the referred optical system is characterized by the absence of some or all of the stepped optics that go with the flow lines, leaving only those portions that cross the flow lines, this is, the heliostats and in which the eventual continuous (not step like) portions of the primary concentrator may also be divided into heliostats.

In another embodiment, the referred optical system is characterized by the heliostats being able to rotate about themselves to track the apparent diurnal motion of the sun.

In another embodiment, the referred optical system is characterized by combining at least two optical systems as those referred above thus forming a concentrator with multiple receivers.

In an embodiment the referred optical system is characterized by the fact that the heliostats being placed on a wave like surface, with cylindrical geometry, substantially corresponding to a curve that optically conserves etendue. In another preferred embodiment, the referred optical system is characterized by the mirrors of the primary concentrator being curved or flat. Still in another preferred embodiment the referred optical system is characterized y the global form of the primary being flat.

Preferably, the referred optical system is characterized by all receivers being substantially at the same height and the angles measured from the vertical that passes through one of the receivers substantially being about 33±10° with the line that, leaving the receiver, passes through the point on the primary that marks the transition between one and two receivers, and about 61±5° with the line that goes through the intermediate point of the primary optics and about 71±5° with the line that passes in another transition point from one to two receivers. In a most preferred way the previous optical system is characterized by the angles as measured from the vertical that goes through one of the receivers being: 32.6° with the line that leaving the receiver, passes through the point on the primary that marks the transition between one and two receivers, of 61.2° with the line that goes through the intermediate point of the primary optics and 71.2° with the line that passes in another transition point from one to two receivers. In a more preferred embodiment the previous optical system is characterized by not comprising secondary concentrators by the receivers.

In another embodiment said optical system is characterized by the receivers having a larger size than they would if sized to correspond to the ideal or maximum concentration.

The present invention also relates to an optical system characterized by comprising transparent covers, substantially perpendicular two flow lines and mirrors (mirrored on both sides) that substantially follow the flow lines, to reduce the convection by the receiver.

In a preferred embodiment of the present invention the referred optical system is characterized by comprising mirrors and/or transparent covers with the shape of broken lines that substantially follow flow lines or are transverse to them and in which the covers may be simple or double.

The present invention refers to the use of any optical system as defined above, characterized by the optical system being intended to concentrating the solar radiation.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the present invention will be apparent from the following more particular description thereof, presented in conjunction with the following drawings wherein:

FIG. 1 shows a parabolic reflector.

FIG. 2 shows a flat mirror reflecting radiation total angular aperture 2θ.

FIG. 3 shows a parabolic reflector cut into several portions and those portions moved down to form a Fresnel reflector. The orientation of these small mirrors then must be adjusted.

FIG. 4 shows a Fresnel reflector.

FIG. 5 shows a schematic view of a Fresnel reflector with an infinite number of infinitely small mirrors.

FIG. 6 shows shading occurring in a Fresnel reflector due to etendue mismatch between the incoming and outgoing radiation.

FIG. 7 shows an incoming beam of light being divided and reflected onto two separate receivers.

FIG. 8 shows the geometry of dividing a beam of incoming radiation into two of outgoing radiation by a tilted surface.

FIG. 9 shows several etendue conserving curves when the incoming light is redirected to two different receivers.

FIG. 10 shows the most compact curve from those shown in FIG. 9.

FIG. 11 shows the possible geometry for a radiation splitter optic, dividing a beam of incoming light into two beams of outgoing light. In this example, the radiation splitter optic is composed of two heliostats.

FIG. 12 shows the shading that may occur within two contiguous radiation splitters, such as that shown in FIG. 11.

FIG. 13 shows the curve in FIG. 10 with radiation splitters in it.

FIG. 14 shows the tangency point on the etendue conserving curve beyond which light redirected towards the left receiver is shaded.

FIG. 15 shows a combination of a parabola and an etendue conserving curve.

FIG. 16 shows the curve in FIG. 15 with simple heliostats and radiation splitters on it.

FIG. 17 shows a comparison between the geometry of the optic in FIG. 16 and a parabola for the same purpose.

FIG. 18A and FIG. 18B show a Fresnel primary with a different ray assignment.

FIG. 19 shows a secondary mirror for a Fresnel primary as shown in FIG. 18.

FIG. 20 shows a central V receiver with a truncated secondary mirror and a Fresnel primary.

FIG. 21 shows the overall geometry of the heliostat field, determined by etendue considerations.

FIG. 22 shows a primary-secondary system for a small acceptance angle.

FIG. 23 shows a detail of FIG. 22 around the receiver area.

FIG. 24 shows a Fresnel lens with different prisms on the right and left halves.

FIG. 25 shows an ideal stepped flow-line concentrator with a linear receiver.

FIG. 26 shows a combination of a Fresnel primary and a truncated flow-line secondary.

FIG. 27A shows an ideal stepped flow-line concentrator with a V receiver.

FIG. 27B shows the construction method of the concentrator in FIG. 27A.

FIG. 28 shows a concentrator for several receivers with Fresnel primary and truncated secondary mirrors.

FIG. 29 shows a concentrator similar to the one in FIG. 28, but designed for a smaller acceptance angle.

FIG. 30 shows a concentrator producing maximum concentration on the receiver, with a discontinuous primary mirror.

FIG. 31 shows the geometry of an ideal (infinite number of infinitesimal heliostats) flat Fresnel primary for two receivers.

FIG. 32 shows the ideal relative dimensions of an ideal flat Fresnel primary for two receivers.

FIG. 33 shows the etendue mismatch across the primary for an ideal flat Fresnel primary for two receivers and with ideal relative dimensions.

FIG. 34 shows the geometry of a concentrator for an acceptance angle 2θ and flat receiver, showing that the receiver is not large enough to accommodate all the etendue emitted by the primary.

FIG. 35 shows an ideal primary-secondary concentrator for a V receiver.

FIG. 36 shows an ideal primary-secondary concentrator for a U receiver.

FIG. 37 shows an ideal primary-secondary concentrator for a receiver made of circular tubes.

FIG. 38 shows a concentrator for a V receiver whose primary has finite size mirrors.

FIG. 39 shows a concentrator for two V receivers whose primary has finite size mirrors and a truncated secondary mirror.

FIG. 40 shows a concentrator for small acceptance angle and two V receivers, whose primary has finite size mirrors and a truncated secondary mirror.

FIG. 41 shows a modification of a V receiver and a secondary mirror that results in a design in which the mirror does not touch the receiver.

FIG. 42 shows a concentrator for an inverted Δ receiver with a smooth secondary minor (with a continuous derivative).

FIG. 43 shows a concentrator for a larger than ideal V receiver. The secondary mirror no longer extends all the way to the end of the primary.

FIG. 44 shows an ideal concentrator for a V receiver and the flow lines (or G-lines) and their perpendicular, or F-lines, inside it.

FIG. 45 shows a primary-secondary in which the receiver is protected by an F-line shaped transparent cover (perpendicular to the flow lines) and with internal mirrors along the flow lines. Both these components reduce internal convection thermal losses.

FIG. 46 shows a V receiver with thermal insulation on the back. The secondary mirror may have a heat dissipater to prevent overheating.

A better understanding of the characteristics and advantages of the present invention will be obtained with reference to the detailed description of the invention and corresponding figures, which are illustrative of the way in which the principles behind the invention are used.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to new etendue-adjusted primary concentrators combined with secondary concentrators, for simple or multiple receptors, able to reach the maximal possible concentration. The present invention also relates to devices able to reduce convective thermal losses from the receivers.

In prior art these concentrators may have only one receiver (as in the case Linear Reflectors of the Fresnel type-LFR) or they may have multiple reflectors (as in the case of Compact Linear Fresnel Reflectors-CLFR). The present invention shows improvements in the general primary shape in the case of multiple receivers. It further shows new concentrators of the primary-secondary type, coming very close to the theoretical concentration limit, even when the primary is formed by large heliostats (something impossible in prior art). These new concentrators are also applicable in the case of multiple receivers. The present invention further shows devices to reduce thermal convective losses from the receiver(s).

The present invention describes a new type of Fresnel primaries so-called “etendue adjusted”. These primary shapes have a wave type configuration, conserving “etendue” and are characterized by the fact that the etendue of the incident radiation is perfectly adjusted to the etendue of the reflected radiation towards the receivers (in particular in the case that only one receiver exists the shape is no longer a wave but a parabola (prior art)).

The corresponding reflector mirror corresponds to a large number of small structures that follow the etendue conserving curve and reflects the light/radiation to the receivers. A limiting case of these new primaries occurs (as in prior art) when they are formed by an infinite number of heliostats. New secondaries can then be designed for these primaries coming close to the theoretical limit for concentration. Although these new sets represent a step ahead when compared with prior art, because of their reduced etendue mismatch, they have a reduced practical interest. As discussed below the present invention also shows geometries for primary structures with large (finite) and practical sizes.

The present invention also describes new primary-secondary concentrators for single receivers. The primary is composed by a set of heliostats (movable mirrors able to track the sun). To increase primary concentration it may be combined with a secondary one. To facilitate the design of a continuous secondary, the heliostats are interconnected by flow lines, resulting in a continuous primary with a stepped shape, a continuous and broken line. A continuous secondary may then be designed for this now continuous primary. A continuous primary is not a necessary condition and a continuous secondary may also be designed even for a discontinuous primary (this type of optics is also described in the patent. However a continuous primary makes the design more intuitive. Once the secondary designed, the primary portions along flow lines can be removed, leaving the primary just with the initial heliostats.

The primary reflector is thus conceived to be a flow line stepped reflector, consisting of continuous of portions, as a broken line, which parts either follow or cross flow lines. These individual portions are curved in general, but some may be flat. The underlying shape of the primary, as a whole, may be curved or flat.

In particular configurations of the present invention, the resulting optics, primary-secondary, comes close to the theoretical concentration limit on the receiver. In contrast, prior art could only (theoretically) reach maximum concentration on the receiver only with a primary of infinitesimal structures. In the primary-secondary set, the primary is conceived to reflect one set of edge rays into directions tangent to the receiver. The other set of edge rays is reflected by the primary into the direction of the secondary and this one, in turn, redirects them in a way that they also end up tangent to the receiver.

In case, for instance, of large solar systems, the sections of stepped reflectors along flow lines, may be eliminated, thus resulting a discontinuous reflector, containing only the portions that cross the flow lines. These portions may now be considered as heliostats that “track” the apparent motion of the Sun. This set by itself is not ideal and the heliostats may be extended a little to recuperate some of the lost radiation. The secondary initially designed for the continuous reflector can now be used with the resulting curved heliostats, constituting high efficiency optics, coming close to the theoretical concentration limit on the receiver.

Some of these concentrators for a single receiver may now be combined, originating concentrators for multiple receivers. The process is similar to that of combining LFR to get CLFR, in which several LFR juxtapose on each other, intersecting and forming a CLFR. In a simpler solution consists on having all heliostats on a straight line. A more elaborated solution the underlying primary shape may be different, just as a curve that conserves etendue. In these optics the heliostats can be placed on a wave shaped line (surface), reflecting solar radiation towards different receivers. The size and shape of the heliostats are a function of their position on the wave line (surface). This method permits matching the incident radiation etendue with the one reflected towards the different receivers. The result is a Fresnel primary with very little blocking, and thus with very small optical losses. In contrast, prior art does not contemplate the matching of the incident etendues to the reflected ones at and by the primary and so the resulting optics are less efficient due to radiation blocking between heliostats.

The present invention also explores the relative dimensions of a reflector optimized for two receivers, in which all components (portions) are placed on a straight line (flat surface). For a final optimal (in the theoretical limit) concentration of the present invention, obtained with the help of the secondary concentrators described in the present invention, the receiver can no longer be flat and have only one absorbing side, as it can no longer accommodate all the reflected radiation etendue from the primary towards it.

The present invention further describes a methodology to create a separation (gap) between the mirror and the receiver, to prevent a thermal bridge and the consequent thermal losses.

The present invention further describes ways to reduce the convective losses around the receiver, through the use of covers/transparent surfaces, substantially perpendicular to flow lines and mirrors that substantially follow those flow lines.

The present invention relates to optical design with two-dimensional geometry, that may be implemented in a practical way applying to these designs a translation symmetry (or a rotational one when only a design with a flat receiver exits).

The term “étendue” of the radiation that crosses a curve (two-dimensional geometry) relates to the integral of the projected length with the angular aperture of the radiation: U=∫∫dxcosθdθ in which U is the étendue, dx is an infinitesimal length along the curve, θ is the angle the propagation direction makes with the normal to dx and dθ the angular aperture occupied by the radiation that crosses dx. In a more general way the curve may be immersed in a medium with refractive index n, and in that case etendue is defined by U=∫∫ndxcosθdθ.

In the present invention the term “etendue matching curve” relates to a curve to which small structures may be added and which redirect the light towards one or more receivers and for which the incident light etendue coincides with the “etendue” of the redirected light towards the receivers.

Additionally, the term “stepped optics” or “optics in steps”, relates to optics that consists of a mirror that follows a flow line, followed by one that crosses the flow lines which captures and re-directs a portion of light and then another mirror along a flow line, followed by another mirror crossing the flow lines capturing and redirecting the light and so on. A particular case occurs when the optics crossing flow lines is a simple mirror (curve or flat). In that case the stepped optics is a continuous mirror, continuous but broken, either following or crossing the flow lines.

The term “simple mirror” relates to any surface with only one reflecting face, and “double mirror” relates to any surface mirrored on both sides thereof.

Further, the term “double cover/transparent surface” relates to one that is formed by two single transparent surfaces.

The present invention will be further clarified with reference to the accompanying figures.

FIG. 1 shows a parabolic mirror 101. Light ray 102 parallel to the axis of the parabola is reflected at point 103 with normal n in direction 104 towards focus 105. The normal to the parabola at point 103 is in direction n. All rays parallel to 102 are also reflected by the parabola towards its focus 105.

FIG. 2 shows a flat mirror 201 and the etendue balance of the light it receives and it reflects. Light comes in vertically with angular aperture 2θ, making an angle α₁ to the normal n to the mirror, and leaves it still with the same angular aperture 2θ, but now making an angle α₂ to its the normal. The middle ray 202 comes in vertically and leaves the mirror as ray 203 making an angle φ to the vertical. The etendue of the incoming radiation is given by dU₁=2dlsinθcosα₁ where dl is the length of mirror 201. Also, the etendue of the light leaving the mirror is given by dU₂=2dlsinθcosα₂. If the angular aperture 2θ is conserved at the mirror, then the conservation of etendue dU₁=dU₂ results in α₁=α₂. Now suppose that this mirror is a very small portion of a curve, such as the one shown in FIG. 1. This condition (also the law of reflection) defines the direction of the normal n to the curve for each value of φ since the middle ray of the incoming radiation is vertical before reflection. If an initial point is given for the curve and the curve concentrates all the middle rays to a focus, then this condition α₁=α₂ results in a parabolic shape. The parabola can then be seen as a shape that conserves the etendue of the radiation when the latter is concentrated to a focus.

FIG. 3 shows a parabola divided into sections. Each one of those sections can be brought down to the plane and adjusted to form a Fresnel reflector.

FIG. 4 shows the Fresnel reflector resulting from the construction in FIG. 3. Now, instead of a parabola, there are a set of Fresnel mirrors 401 on the plane that concentrate the light to the focus 402. The Fresnel mirrors in this figure are large compared to the overall size of the optic and, if a sharp focus is needed, then the mirrors must, obviously, be curved.

FIG. 5 shows a schematic view of the case in which the Fresnel mirrors in FIG. 4 get smaller and smaller. In the limit case of an infinite number of infinitely small mirrors, the Fresnel reflector would be a microstructure 502 that reflects vertical rays to the focus 503. For each point 501 on the microstructure, the reflected ray makes an angle φ to the vertical. For a sharp focus of a set of vertical parallel rays onto focus 503, as the Fresnel mirrors get smaller and smaller, their curvature may decrease. In the limit case shown in the figure, these mirrors would be flat.

FIG. 6 shows the etendue mismatch for the incoming and outgoing radiation in a Fresnel reflector and the consequent and inevitable shading of light. This is the situation at point 501 of the Fresnel reflector in FIG. 5. The etendue of the incoming radiation is dU₁=2dlsinθ while that of the outgoing radiation is dU₂=2dlsinθcosφ where dl is the length of aperture 602 (the projection of 602 in direction φ is da=dlcosφ). We can then see that etendue is no longer conserved. The lost etendue corresponds to shading by adjacent Fresnel mirrors. Only the vertical light rays between 606 and 607 are reflected towards the receiver, and those between 605 and 606 are shaded by the mirror to the left. From these considerations, it can be concluded that not all the light received at point 501 in FIG. 5 can be redirected towards receiver 503. This means that either part of the light is lost (to shading/blocking) or it must be redirected somewhere else. In order to redirect the excess light somewhere else we need another receiver and, therefore, we are lead to consider a multi-receiver Fresnel reflector.

FIG. 7 shows the geometry of a point 707 on a Fresnel reflector with two receivers 703 and 704. An incoming vertical beam of light hits point 707 on the Fresnel reflector and is split in two separate beams: a beam 705 redirected to the left towards receiver 703 and another beam 706 redirected to the right towards another receiver 704. These beams make, respectively, angles φ₁ and φ₂ to the vertical.

FIG. 8 shows a detail of what occurs at point 707 in FIG. 7. In a neighbourhood of that point, the Fresnel reflector can be seen shaped as an infinitesimal flat line 801 of length dl tilted by an angle α to the horizontal. Just like we did above for the case of the parabola, also here we consider that the incoming radiation has angular aperture 2θ and that also the redirected beams have the same angular aperture. The etendue of the radiation 804 received by 801 (incoming radiation) is given by dU₀=2dlsinθcosα. The etendue of the radiation 805 redirected to the left is dU₁=2dlsinθcos(φ₁−α) and that of the radiation 806 redirected to the right is dU₂=2dlsinθcos(φ₂+α). Conservation of etendue can be written in this case as dU₀=dU₁+dU₂ or cos(φ₁−α)+cos(φ₂+α)=cosα. Now, from the geometry in FIG. 7 and the position of point 707, angles φ₁ and φ₂ can be determined. From the previous equation it is then possible to determine angle α that the Fresnel reflector makes to the horizontal at that point. Given an initial point for the Fresnel reflector, a curve can be obtained that conserves the etendue of the light redirected towards receivers 703 and 704. This is a similar process to that used to define the parabola above (in the case of a single receiver).

In the case in which the incoming radiation 804 has angular aperture 2θ₀, the radiation 805 redirected to the left has angular aperture 2θ₁ and the radiation 806 redirected to the right has angular aperture 2θ₂ the shape of the etendue-conserving curve is governed by the equation for the conservation of etendue that can now be written as: sinθ₁cos(φ₁−α)+sinθ₂cos(φ₂+α)=sinθ₀cosα.

FIG. 9 shows three etendue conserving curves 902, 903 and 904 calculated according to the method described in FIG. 7 and FIG. 8 for three different initial points 905, 906 and 907, all on the vertical of the receiver 909. For midpoint 901 the condition φ₁=φ₂ is verified. The equation for etendue conservation cos(φ₁−α)+cos(φ₂+α)=cosα results in α=0 and also in φ₁=φ₂=α°. Point 901 may thus be obtained if the distance between receivers 908 and 909 is given (in this example they are assumed to be at the same height). The most compact etendue-conserving curve is 902 starting at point 905 at the same height as 901.

FIG. 10 shows curve 1001 that is the most compact etendue-conserving curve of FIG. 9. It also shows the geometry of a vertical incident beam which splits at point 1006 into the beam 1004 redirected to the left towards receiver 1002 and into the beam 1005 redirected to the right towards receiver 1003. The angles these redirected beams make with the vertical are φ₁ and φ₂ respectively.

FIG. 11 shows a radiation splitter optic, splitting the incident beam in two beams. This optic may now be applied in point 707 of FIG. 7, a detail of which is shown in FIG. 8, allowing for the incident beam to be split in two reflected beams. The incident light is split in two parts: 1104 and 1105. The light in 1104 is reflected by mirror 1102 to the left in direction 1106. Besides, the light in 1105 is reflected by the mirror 1103 to the right in direction 1107. The inclined line 1101 projects up as a combination of lengths 1104 and 1105. The area 1104 of light after reflection is the same area 1104 before reflection. Likewise, area 1105 of the light after reflection is the same as the area 1105 before reflection.

FIG. 12 shows two radiation splitters on a straight line. Each radiation splitter is composed of a mirror 1201 and a mirror 1202. This geometry produces a small blocking/shading 1203 for the light reflected by mirrors 1201 to the left. There is also some blocking/shading for the light reflected by mirrors 1202 to the right. This combination of splitting optics may also be applied over an etendue conserving curve.

FIG. 13 shows the same etendue-conserving curve of FIG. 10 but now with radiation splitters 1303 on it. These optics redirect light towards receivers 1301 and 1302.

FIG. 14 shows etendue-conserving curve 1401, the same as shown in FIG. 10. There is point 1404 on this curve which tangent intersects receiver 1402. To the right of this point, light reflected towards 1402 is shaded by the curve to the left. This defines a maximum rim angle 1405 at receiver 1402. The situation is symmetrical for receiver 1403. The portion of the curve between points 1404 and 1407 (like the rest of the curve) was conceived so that the radiation impinging on it was redirected to receivers 1402 and 1403. However, because of the referred blocking/shading effect, the radiation that would be reflected towards receiver 1402 would not reach it. It would then make more sense to have the portion of the curve between 1404 and 1407 reflect radiation towards receiver 1403. This change originates a readjustment of the design of the whole reflecting primary profile.

FIG. 15 shows a combination of a parabola and an etendue conserving curve for two receivers. This combination is a consequence of the arguments presented in FIG. 14. Since the parabola is an etendue conserving curve for one receiver, the hole curve conserves etendue. The parabolic portion of the curve reflects light onto a single receiver while the remaining etendue conserving curve reflects light to two receivers. Portion 1501 of the curve between points 1507 and 1508 is etendue conserving for two receivers 1502 and 1503. Portion of the curve to the right of 1505 is a parabola with focus 1503 and portion of the curve to the left of point 1507 is a parabola with focus 1502. Accordingly a vertical light beam hitting point 1505 on the parabolic portion of the curve is reflected towards receiver 1503 while a light beam hitting point 1504 on the etendue conserving curve for two receivers is split into two beams redirected towards receivers 1502 and 1503. The rim angle of the primary as seen from the receivers is angle 1509. There is a small angle 1506 of the Fresnel reflector spanning an angle of 1.5 deg that is not visible from the receiver. In a particular case, the parabola to the right of point 1508 is such that its tangent at that point intersects the receptor 1502. The point 1508 serves as an initial point for the construction of the remaining etendue conserving curve for two receivers, which extends from here to point 1507.

FIG. 16 shows the curve of FIG. 15 with heliostats and radiation splitters 1601 on it. The parabolic portion of the curve has simple heliostats while the etendue conserving for two receivers has radiation splitters. Receivers are at positions 1602 and 1603.

FIG. 17 shows a comparison between the curve in FIG. 15 and the corresponding parabola. The etendue conserving curve 1701 has a height 1705 for receivers 1702 and 1703 at a height 1704. As a comparison, parabola 1706, for the same rim angle as the etendue conserving curve, has a height 1707. Height 1705 is 15% of height 1704 of the receivers and is 14% of the height 1707 of the corresponding parabola.

FIG. 18A and FIG. 18B show a different design for a Fresnel primary with a different ray assignment. The right edge rays parallel to 1810 are reflected in directions tangent to the receiver. In this example, the receiver is V-shaped with end points 1801 and 1803 and vertex 1802. The description below, however, is also valid in the case in which the receiver has some other convex shape, provided that the shape of the curves in the Fresnel reflector is defined accordingly.

This is a common procedure when designing nonimaging optics. The right receiver 1831 has the same shape as the left one (bound by points 1801, 1802 and 1803).

For this particular shape of receiver, the Fresnel reflector curve starts with a parabola 1804 with axis parallel to 1810 and focus 1801. The vertical though point 1805 is the same as through point 1802. The Fresnel reflector then continues between points 1806 and 1808 as another parabola 1807, also with axis parallel to 1810, but now with focus 102. The central portion of the Fresnel receiver is an etendue conserving curve 1821 for two receivers, extending from point 1808 to its symmetrical 1822. With reference to a generic point 1823 on this curve, the light reflected to the left receiver 1830 is bound by ray 1826 tangent to the receiver at point 1802 and by the other edge ray 1827. The light reflected to the right receiver 1831 is bound by ray 1824 tangent to the receiver at point 1820 and by the other edge ray 1825. This portion of the curve is calculated using a similar geometry to that shown in FIG. 8, but where now rays 807 and 808 correspond to rays 1824 and 1826.

As point 1823 moves towards point 1808 where curve 1821 ends, ray 1824 tends to ray 1828. This ray 1828 is tangent to curve 1821 at point 1808. Choosing a point 1808 further up on curve 1807 to start curve 1821 would result in less compact Fresnel primary. On the other hand, choosing a point 1808 further down on curve 1807 to start curve 1821 would result in light losses due to shading of some light by curve 1821 (in this case, ray 1828 would intersect curve 1821).

It is possible to determine how much etendue is reflected by the Fresnel mirror in the direction of the left receiver 1830 and how much is reflected in the direction of the right receiver 1831. All the light falling on parabolas 1804 and 1807 is redirected in the direction of 1830 (although in the present configuration not all this light will hit the receiver). On the other hand, for the light hitting curve 1821 between points 1808 and 1822, half of it is reflected towards 1830 and the other half towards 1831. This means that the light redirected in the direction of 1830 by the Fresnel reflector on 1821 corresponds to the etendue of the light falling on half the curve 1821. The total etendue of the light redirected towards 1830 is then given by U=2Rsinθ where R is the horizontal distance between point 1805 and midpoint 1829 of curve 1821.

FIG. 19 shows a secondary mirror 1901 for a Fresnel primary, such as the one in FIG. 18, further increasing its concentration. The secondary mirror 1901 is designed in such a way that left edge rays 1809, after being reflected at the primary, are redirected by the secondary in a direction tangent to the receiver 1830. In this example of a V receiver, this means that these edge rays are redirected towards the edge 1802 of receiver 1830. This condition defines each point 1902 on the secondary mirror. The secondary mirror starts at edge 1803 of receiver 1830 and extends all the way to the endpoint 1822 of curve 1821. The concentration this optic produces on the receiver is the maximum allowed by conservation of etendue and, therefore, the concentrator is ideal. These secondaries are known as TERC (Tailored Edge Ray Concentrators). Unfortunately, in this geometry, the secondary completely shades the primary and it must, therefore, be truncated to be usable, otherwise no light would reach the receiver.

FIG. 20 shows the complete shape of a primary Fresnel reflector for a V receiver 1830, combined with a truncated secondary mirror 2001. The Fresnel primary is shaped as curves 1804, 1807 and 1821 to the right and by their symmetrical 2002, 2003 and 2004 to the left of receiver. The receiver receives light from the points on the primary between point 1822 on the right and its symmetrical 2005 on the left.

Due to secondary truncation, now some light is lost because part of the secondary mirror is no longer there to redirect it towards the receiver. The final concentration of the optic also decreases accordingly. The receiver and the secondary mirror also shade the primary, further decreasing the final concentration. For small acceptance angles such as those needed for the collection of sunlight, these losses are rather small.

If the system had no losses, the etendue of the light reaching receiver 1830 would equal that of the light falling on the primary between point 1829 and its symmetrical 2006.

This optical system is extended left and right by reflection symmetry with 2007 and 2008 as the axes of symmetry.

FIG. 21 shows the geometry used to derive the overall dimensions of the primary-secondary optic. The positions of points 1801 and 1803 are first defined (in this example they are at the same height). Given the total acceptance angle 2θ, point 1805 can be determined. The geometry now has two unknowns: the length L of each side of the V receiver and the distance R from point 1805 to the midpoint 1829 of the heliostat field. The condition is imposed that point 1829 is at the same height as 1805 to ensure primary compactness. These two unknowns L and R can be determined by imposing the equations of etendue balance at point 1829 and between the heliostat field and the receiver. Just like in the case of the primary in FIG. 9, also here the condition of conservation of etendue at point 1829 results in φ=60° and, therefore, β=60°−θ. The conservation of etendue between the heliostat field and the receiver is 2L=2Rsinθ. These two conditions determine L and R.

FIG. 22 shows an optic similar to that in FIG. 20, but now designed for an acceptance angle of ±0.01 rad (total acceptance angle of 1.15°. The primary is now curve 2201 and the secondary is curve 2202.

FIG. 23 shows a detail of FIG. 22, showing the V receiver 2301 and truncated secondary mirror 2202, also shown in FIG. 22. The concentration of the optic in FIG. 22 is 87% of the theoretical maximum with an efficiency of also 87%. These results already account for the shading that the receiver 2301 and secondary mirror 2202 produce on the primary. The optics shown from FIG. 18 to FIG. 23 assume the primary is formed by an infinite number of infinitesimal structures. This is a severe practical limitation. However, it is possible to design primary-secondary combinations in which the structures on the primary have a finite dimension.

FIG. 24 shows a Fresnel lens which left and right halves are different. Similar principles to those used in the design of this lens will be used in the following figures for the design of the finite size structures to place over the form of the primary. To the right of the vertical line 2401 the bottom surface of the lens has the form of a continuous but broken line, which portions 2402 follow flow lines 2403 of the incident radiation, while portions 2404 cross those flow lines.

To the left of the vertical line 2401, the bottom surface is also a broken line but now designed in a different way. The lines 2412 are parallel to the edge rays 2413 inside the lens (and, thus, have no optical function) while lines 2411 cross the flow lines of the incident radiation.

FIG. 25 shows a primary-secondary concentrator with an acceptance angle 2θ and a single receiver 2501 with edges 2502 and 2503.

In this example, the primary is formed of a parabolic mirror 2504, a flat flow-line mirror 2505, and another mirror composed of two sections: a flat section 2506 and a parabolic section 2507. These two sections (2506 and 2507) share a common derivative at point 2513. Both parabolas (2504 and 2507) in the primary have axes parallel to edge rays 2517 and focus 2502.

The secondary is formed of three sections 2508, 2509 and 2510. An edge ray coming from the left is reflected at a point 2511 on parabolic section 2504 in the primary towards a point 2512 on the secondary. This point is calculated in such a way that it reflects that ray towards the edge 2502 of the receiver. For the reflected edge rays at point 2513 of the primary, one goes into direction 2514, while the other is reflected again by the flow-line 2505 into the direction 2515, parallel to 2514. The parabolic arc 2509 with axis parallel to 2514 and 2515 concentrates these edge rays towards edge point 2502 of the receiver. Points 2516 in section 2510 of the secondary are calculated in such a way that they reflect towards the edge 2502 of the receiver the edge ray they get from the primary parabolic arc 2507. Primary and secondary meet at point 2518.

Flow-line 2505 and section 2506 may be given different shapes according to the anidolic optics principles (nonimaging optics). In this case the secondary section corresponding to the primary will no longer be parabolic, but will be calculated with the edge ray principle of anidolic optics.

This optic produces the maximal concentration on the receiver. Radiation incident directly on the mirror that follows the flow line 2505 is reflected into directions other that those of the receiver, but all other light is ideally concentrated on the receiver.

As in the above-mentioned cases, the secondary must be truncated so that radiation may reach the primary.

This combination of primary and secondary is a stepped flow-line optic with walls following flow lines, as the primary is obtained with mirrors generated and placed along flow lines, in a successive way and alternating with other that cross the flow lines. In the limiting case these structures, portions, of primary become infinitesimal and the secondary becomes what is known as a TERC for that primary.

This method for producing the primary shares principles similar to those used in designing the right half of the Fresnel lens, shown in FIG. 24.

FIG. 26 shows a primary-secondary concentrator with one receiver only 2601. The primary is similar to the one shown in FIG. 25, only with more steps. Mirrors 2505 along the flow lines have been removed, leaving only mirrors 2603 in the primary to reflect light/radiation. Each one of these mirrors 2603 is composed of two sections as in FIG. 25. The secondary 2602 was also truncated so that light/radiation may reach the primary.

Since mirrors 2505 along the flow-lines have been removed, section 2506 of the mirror of the primary (as shown in FIG. 25) can now be slightly extended to the left to recuperate some light/radiation. Once the mirrors along the flow-lines are eliminated, the primary is no longer ideal.

FIG. 27A shows the same construction as FIG. 25 in which receiver 2720 has, in this example, V-shape in which the primary portions 2701 follow the curve 2721. In this example the curve has the same shape as that of FIG. 19, and conserves the etendue of light/radiation reflected towards two receivers. The primary is formed by mirrors 2702 along the flow lines and mirrors 2703 across the flow lines. These mirrors 2703 are also formed of two sections, just as in FIG. 25. The secondary mirror 2704 starts at the tip 2705 of the receiver 2720 and ends at point 2706 where it meets the primary.

FIG. 27B shows the construction of the primary-secondary mirrors, the same as in FIG. 25. An edge ray coming from the right and incident on one of the top points of a mirror 2703 is reflected as ray 2712, tangent to the receiver at point 2708. The edge ray coming from the left and reflected at the same point of the primary, generates ray 2713, reflected in turn at the secondary mirror at point 2714 and in a direction tangent to the receiver at point 2708.

An edge ray coming from the left and hitting a low point on another primary mirror 2703 is reflected in direction 2709. On the other hand, the edge ray coming from the right and reflected at the same point on the primary is once again reflected by mirror 2702 along the flow line in a direction 2710, parallel to 2709. Both these rays 2709 and 2710 are redirected towards directions tangent to the receiver at point 2708 by parabolic arc 2711 on the secondary mirror.

FIG. 28 shows a primary-secondary optic with two receivers. It is obtained from the construction in FIG. 27A. Flow line mirrors 2702 are eliminated, leaving only the primary mirrors 2703. Mirrors 2703 are then duplicated by reflection symmetry with 2707 as symmetry axis, thus originating the 2801 primary section. Section 2803 may also be divided into smaller mirrors, simply by cutting it with vertical lines. The concentration produced by the primary mirror is augmented by secondary 2802.

This optical system is also extended left and right by reflection symmetry with 2804 and 2805 as symmetry axes.

FIG. 29 shows a best embodiment of the present invention. It shows a concentrator similar to that of FIG. 28, but designed for a smaller acceptance angle of ±0.01 rad. It has an efficiency of about 85% and attains 85% of the maximum possible concentration. This result already accounts for the shading the secondary and receiver produces on the primary.

Vertical line 2902 corresponds to vertical line 2707 in FIG. 28. Line 2901 corresponds to the symmetrical of line 2707 relative to symmetry axis 2804. This optical system is extended left and right by reflection symmetry with 2901 and 2902 as the axes of symmetry. It is to be noted that if 2901 and 2902 are vertical flat mirrors, this optic behaves like a concentrator for a V receiver.

FIG. 30 shows another example of the present invention with a primary alternative to that of FIG. 25. The design in both figures is quite similar, except for the small flat mirror 2506 that is now replaced with a larger flat mirror 3001 and for the flow line 2505 that is not shown in this FIG. 30.

This optic still produces maximum concentration on the receiver 3002. All light falling on the space between end points 3003 and 3004 of the primary mirrors is lost. Also, all the light hitting a point 3005 on mirror 3001 and reflected in directions contained between 3006 and 3007 is shaded by mirror 3008 and lost. The size of the receiver is such that the etendue it can receive matches that reflected by the whole primary (left and right halves) towards it. When that happens, the secondary touches the primary at its end point 3009.

The geometry in this figure may also be considered an alternative to that in FIG. 25 for the design of the secondary. It may be noted that the secondary obtained for this new discontinuous primary is the same as the one obtained for the continuous primary of FIG. 25. It can therefore be seen that a continuous primary is not a necessary condition for the design of a continuous secondary.

Like in the case of the secondary in FIG. 25, portion 3010 of the secondary mirror is a parabola with axis parallel to rays 3012 and focus at the opposing edge 3011 of the receiver. Portions 3013 and 3014 of the secondary are calculated the same way as in FIG. 25.

This construction of the primary shares similar principles to those used in the design the left half of the Fresnel lens shown in FIG. 24, in which now the surface without optical function 2412 correspond to mirrors without optical function and have been removed.

FIG. 31 shows a concentrator for two receivers, but in which the primary instead of being wave-shaped as in the two previous cases is now straight or flat. This Figure shows an ideal flat Fresnel primary extending from 3103 to 3109 for two point receivers 3101 and 3102. By ideal it is meant a primary with an infinite number of infinitesimal structures. From point 3103 to point 3105 light is reflected towards receiver 3101 only. Between points 3105 and 3108, light is reflected towards both receivers 3101 and 3102. In this example, it is considered that the optical system is symmetric relative to the vertical through midpoint 3107.

Reflection of light by the Fresnel mirror is such that the bisector to the edge rays points towards points towards 3101 (or 3102).

For a point 3104 between points 3103 and 3105 on the reflector, the etendue mismatch between that of the incoming radiation and that of the reflected light towards receiver 3101 is given by ΔU₁=2sinθ(1−cosφ₁)dx. For another point 3106 between points 3105 and 3108, the etendue mismatch between that of the incoming light and that ideally reflected towards receivers 3101 and 3102 is |ΔU₂|=2sinθ|1−cosφ₁+cosφ₂|dx where |α| is the absolute value of α. The absolute value in the expression for ΔU₂ ensures that the etendue mismatch is always accounted for as a positive quantity when integrating it across the Fresnel reflector. From these expressions it can be seen that the etendue of the incoming radiation does not match what ideally the Fresnel reflector should emit towards the receivers. The parameters of the optical system must then be adjusted in such a way as to minimize this etendue mismatch. The height of the receivers (distance from point 3103 to 3101) may be considered as a scale factor of the whole system and, therefore, it can be made equal to one. Being the receivers at a different height, the whole system would be scaled accordingly. The parameters that must now be adjusted are the distance between receivers (distance from 3101 to 3102) and the horizontal coordinate x_(T) of the transition point from one to two receivers.

The total etendue mismatch is proportional to the integral of ΔU₁+|ΔU₂| from x₀ (point 3103) to x_(M) (point 3107). This integral must be minimized relative to the parameters of the optic: horizontal coordinate x_(T)and distance between receivers.

FIG. 32 shows the overall relative dimensions of an optimized Fresnel primary when all the reflectors are on the same plane. Angle α_(T) from the vertical through the receiver 3101 to the transition point 3105 from one to two receivers is α_(T)=32.647°. Angle α_(M) from the vertical through the receiver 3101 to the middle point 3107 of the primary is α_(M)=61.2353°. This makes D=3.643 H where H is the height of receivers 3101 and 3102 and D the distance between them. Receiver 3101 receives light from the right side from point 3103 to point 3108. The rim angle α_(R) measured from the vertical through the receiver 3101 to point 3108 is given by α_(R)=71.58°.

FIG. 33 shows the etendue mismatch across the primary for the optimized geometry in FIG. 32, Horizontal axis 3301 has coordinate x representing the distance across the primary and vertical axis 3302 has coordinate U representing the etendue mismatch for each point on the primary. This figure represents etendue mismatch per unit incoming etendue. The available etendue per available unit etendue is clearly unity across the whole Fresnel primary and is represented as horizontal line 3303 with U=1.

For points 3104 on the primary between point 3103 and 3105, the etendue that the Fresnel reflector should emit towards receiver 3101 is given by 2sinθ cosφ₁dx and the etendue of the incoming radiation is 2sinθdx. Therefore, per unit incoming etendue, the primary should emit an etendue of cosφ₁. This is represented by curve 3304.

For points 3106 on the primary between point 3105 and 3108, the etendue that the Fresnel reflector should emit towards receivers 3101 and 3102 is given by 2sinθ(cosφ₁+cosφ₂)dx and the etendue of the incoming radiation is 2sinθdx. Therefore, per unit incoming etendue, the primary should emit a etendue of cosφ₁+cosφ₂. This is represented by curve 3306.

Curve 3305 is symmetrical to 3304 relative to the midpoint of the Fresnel reflector.

Comparing the curves 3304 and 3306 representing the etendue of the light the Fresnel reflector should emit towards the respective receivers with straight line 3303 representing the available etendue at each point, it can be seen that there are points with excessive etendue available and other points with etendue deficit. For the points to the left of 3105, the etendue that the reflector should emit towards receiver 3101 is less than the etendue available (line U=1). This means that some etendue must be lost at the reflector and there will be shading between the microstructures of the primary (infinitesimal heliostats). On the other hand, for points on the Fresnel reflector between 3105 and 3108, curve 3306 sometimes is above line 3303. This means that the etendue the Fresnel reflector should be emitting towards receivers 3101 and 3102 is more than the etendue available. This means that, as seen from the receivers, the Fresnel reflector will have “dark holes” that do not emit light. For the region in which curve 3306 is below 3302, the needed etendue is less than what is available and there is shading of light at the Fresnel reflector.

Point 3105 for which there is a transition from one to two receivers, the vertical distance between curve 3306 and 3303 and between curve 3304 and 3303 are equal to each other and given by 3307, with a value of 0.158 (or 15.8%).

FIG. 34 shows the geometry of a concentrator for an acceptance angle 2θ. Once the overall geometry of the optical system has been determined (as shown in FIG. 32), the acceptance angle 2θ of the optic determines the width of the receiver as the distance between points 3401 and 3402 (in general, the edge rays are tangent to the receiver). If the receiver was flat between those two points, it could not accommodate all the etendue emitted by a large Fresnel reflector spanning from 3103 to 3108 and its symmetrical. This means that the receiver cannot be flat, but must have some kind of convex shape so that its length is able to accommodate all the etendue emitted towards it by the Fresnel reflector. A possibility (although by no means the only one) is to have a V shaped receiver.

FIG. 35 shows a concentrator for a V receiver 3501 formed of an ideal primary and a secondary. The primary is made of an infinite number of infinitesimal structures and spans from point 3103 to 3108. The secondary 3502 starts at the edge of the receiver and extends to the end 3108 of the primary. The paths of some edge rays 3503 are also shown.

FIG. 36 shows a concentrator similar to the one shown in FIG. 35, but now for a U receiver. The receiver has flat walls 3601 and curved bottom 3602. Edge rays 3603 are reflected in directions tangent to the receiver.

FIG. 37 shows another concentrator similar to the one in FIG. 36 but in which the receiver is now made of a set of circular tubes. The tubes are tangent to the U shaped receiver 3701. Other shapes of receivers are possible using the same design methods.

FIG. 38 shows a concentrator for a V receiver 3801 composed of a primary 3802 and a secondary 3803. The overall geometry of the optic is based on that in FIG. 35, but now the primary has finite size structures, designed according to the method shown in FIG. 25. Those structures can also be designed according to the method shown in FIG. 30. The secondary 3803 starts at the edge of the receiver and extends to the end of the primary.

Flow lines 3805 can now be removed and mirrors 3806 given mirror symmetry about vertical line 3804 thought midpoint 3107.

The primary reflects one set of edge rays tangent to the receiver. In the case of a V receiver, this means that to the left of point 3807 one set of edge rays is concentrated to point 3808, while to the right of 3807, this same set of edge rays is reflected towards point 3809. The other set of edge rays is concentrated to point 3809 after reflection on the secondary 3803. Point 3807 is in this example on the straight line through points 3808 and 3809.

FIG. 39 shows the concentrator obtained by removing the flow lines and mirroring the remaining mirrors about the vertical through point 3107. In this process there are mirrors that intersect or shade other mirrors. The portions of the mirrors above the intersections or portion of mirrors that shade other mirrors are trimmed. This results in a primary which heliostats do not intersect or shade each other.

The primary 3901 now reflects light to both V receivers and the secondary 3902 was truncated to allow light to reach the primary.

FIG. 40 shows a concentrator similar to that in FIG. 39, but designed for a smaller acceptance angle of ±0.01 rad.

FIG. 41 shows a secondary mirror and a receiver. FIG. 41A shows one such configuration with a secondary mirror 4101 and a V receiver 4102. The mirror touches the receiver at its end points 4103. This may be a problem since the receiver may get very hot during operation of the solar concentrator and this contact may heat excessively the mirror damaging it and also creates a heat sink through which heat can escape, reducing the efficiency of the system.

FIG. 41B shows a modification of the geometry in FIG. 41A in which the V receiver is now replaced with an equivalent inverted Δ receiver 4106. The secondary mirrors are now extended by two circular arcs 4105 with centres 4104 and its symmetrical. Now there is only one point of contact between the secondary mirror and the receiver at the midpoint of the top surface 4107. The secondary for triangular receiver has a discontinuous derivative (kink) at point 4103.

FIG. 41C shows a modification of the geometry in FIG. 41B in which the top flat surface 4107 of the receiver was removed and replaced with a concave surface 4109. This new surface may be circular with centre 4110. Now there is no contact between the secondary mirror and the receiver. Concentration, however, is smaller because the surface area of the receiver is larger. If, however, the receiver was a perfect back body, the emission of concave surface 4109 would be equivalent to that of flat surface 4107 and therefore the concentrator would behave as if it had ideal concentration (considering only radiative losses).

FIG. 42 shows another embodiment of the present invention, a concentrator for an inverted Δ receiver but with a smooth secondary mirror (continuous derivative). The portion of the primary between points 4201 and 4202 concentrates one set of edge rays to point 4204 above the secondary mirror. These edge rays are then concentrated to lower tip 4205 of the inverted Δ receiver by hyperbolic arc 4206 with foci 4204 and 4205. Hyperbolic arc 4209 is symmetrical to 4206 relative to the vertical line through the lower tip 4205 of the receiver. The secondary mirror also has a circular arc 4211 with centre in 4207.

The other set of edge rays reflected by the primary between points 4201 and 4202 is concentrated to the lower tip 4205 of the receiver by a portion of the secondary to the right of hyperbolic arc 4209. This portion of the secondary mirror is designed in the same way as the portion of the secondary mirror touching receiver 3501 in FIG. 35.

The portion of the primary between points 4202 and 4203 concentrates a set of edge rays to lower tip 4205 of the receiver, while the other set of edge rays is reflected by the secondary mirror towards the lower tip 4205 of the receiver. Again this is similar to the design of the right portion of the secondary mirror in FIG. 35.

FIG. 43 shows a concentrator similar to that in FIG. 39. Now the lower tip 4301 of the V receiver was moved down from its ideal position, increasing the size of the receiver. The resulting secondary 4302 no longer extends all the way to the end of the primary. Depending on how much the receiver size is increased, it may or may not be necessary to truncate the secondary mirror for optimum operation. The resulting concentrator has a higher efficiency, since more light is now collected by the secondary, but at the cost of a lower concentration, since the receiver has now increased in size.

FIG. 44 shows a concentrator similar to that in FIG. 35 for a V receiver 3501. This figure shows flow lines (or G-lines) 4401 and their perpendicular, or F-lines, 4402. G-lines bisect the edge rays at each point and point in the direction of propagation of light. F-lines also bisect the edge rays at each point, but point in the direction perpendicular to the propagation of light and are, therefore, also perpendicular to the G-lines at each point.

FIG. 45 shows a preferred embodiment of the present invention and shows the concentrator of FIG. 44 with a truncated secondary 4502. Receiver 3501 is now protected by a transparent cover 4503 shaped as an F-line. This shape minimizes the incidence angles of light on the transparent cover and, therefore, minimizes Fresnel reflection losses. F-lines may sometimes be well approximated by simple shapes, such as circumferences.

Between the transparent cover and the receiver, there are mirrors 4504, mirrored on both sides, shaped as G-lines (or flow lines). These mirrors do not affect the flow of light and, therefore, do not affect the optical behaviour of the optic. G-lines may sometimes be well approximated by simple shapes, such as straight lines.

Both the transparent cover 4503 and the internal mirrors 4504 help reduce the convection around the receiver, reducing thermal losses.

The primary extends from point 3108 on the right to point 4501 on the left. These edge points of the primary are symmetrical relative to midpoint 3103.

FIG. 46 shows another embodiment of the present invention. It shows the V receiver of FIG. 45, but with the curved transparent cover 4503 now replaced by a facetted transparent cover. In this example, this faceting has only two facets, resulting in a V transparent cover 4601. The tilt of these flat transparent covers is calculated in such a way as to minimize the average angle 4602 between G-lines (flow line) 4404 and the normal 4603 to transparent cover 4601.

Also internal mirrors (mirrored on both sides) 4504 placed along the G-lines help reduce internal convection.

Thermal losses are further reduced by using thermal insulation 4604 on the back of the V receiver. Overheating of the secondary mirrors may be prevented by using heat dissipaters 4605. At point 4606 there should also be some thermal insulation between the receiver and the secondary mirror to prevent a thermal bridge between the two, resulting in a thermal loss.

The preceding description of the presently contemplated best mode of practicing the invention is not to be taken in a limiting sense, but is made merely for the purpose of describing the general principles of the invention. The full scope of the invention should be determined with reference to the claims. 

1. An optical system with primary concentrator of the Fresnel type and adjacent secondary concentrator, being the secondary receiver set above the primary, and characterized by the primary concentrator containing a stepped flow-line which shape verifies the condition that it reflects a set of edge rays so as to make them tangent to the receiver and the other set of edge rays in the direction of the secondary concentrator, which shape verifies the condition that it, on its turn, reflects the edge rays it receives from the primary concentrator in directions tangent to the receiver, producing there, theoretically, a maximum concentration, and in which the secondary is truncated.
 2. The optical system of claim 1, characterized by the receiver having a face of convex shape and also a flat face, and in which the secondary concentrator touches this flat face only on one point and in which this flat face can be replaced with a concave one, resulting in a secondary which does not touch the receiver.
 3. The optical system of claim 1, characterized by some or all of the portions of the stepped flow-line optic which follow the flow lines being absent, leaving only those portions which cross the flow lines, that is, the heliostats, and in which the continuous portions that may exist (not stepped) of the primary concentrator are also divided into heliostats.
 4. The optical system of claim 1, characterized by the heliostats being able to rotate around themselves to follow the apparent daily motion of the sun.
 5. (canceled)
 6. The optical system of claim 1, characterized by the heliostats being placed on a wave shaped surface, with cylindrical geometry, corresponding, basically, to a curve that optically conserves etendue.
 7. The optical system of claim 6, characterized by the heliostats of the primary concentrator being flat or curved.
 8. The optical system of claim 6, characterized by the overall shape of the primary concentrator being flat.
 9. The optical system of claim 8, characterized by all the receivers being substantially at the same height and the angles measured from the vertical through one of the receivers being about 33±10° with the line which, starting at the receiver, crosses the point of the primary which marks the transition between one and two receivers (angle α_(T)), of 61±5° with the line that crosses the midpoint of the primary optic (angle α_(M)) and of 71±5° with the line that crosses the other point of transition from one to two receivers (angle α_(R)).
 10. The optical system of claim 9, characterized by the angles measured from the vertical which crosses one of the receivers being: 32.6° with the line that, starting at the receiver, crosses the point of the primary that marks the transition between one and two receivers, of 61.2° with the line that crosses the midpoint of the primary optic and of 71.2° with the line that crosses the other point of transition from one to two receivers.
 11. The optical system of claim 6, characterized by not having secondary concentrators next to the receivers.
 12. The optical system of claim 1, characterized by the receivers having a larger size than that they would have if dimensioned for maximum or ideal concentration.
 13. The optical system of claim 1, characterized by comprising transparent covers substantially perpendicular to the flow lines and mirrors (mirrored on both sides) which substantially follow the flow lines for convection reduction next to the receiver.
 14. The optical system of claim 13, characterized by comprising mirrors and/or transparent covers, shaped as broken lines which substantially follow the flow lines or are substantially perpendicular to them, respectively, and in which the covers may be simple or double.
 15. (canceled)
 16. An optical system characterized by combining by means of intersecting at least two optical systems chosen from: an optical system with primary concentrator of the Fresnel type and adjacent secondary concentrator, the secondary receiver set being above the primary, and characterized by the primary concentrator containing a stepped flow-line optic which shape verifies the condition that it reflects a set of edge rays so as to make them tangent to the receiver and the other set of edge rays in the direction of the secondary concentrator, which shape verifies the condition that it, on its turn, reflects the edge rays it receives from the primary concentrator in directions tangent to the receiver, producing there, theoretically, a maximum concentration, and in which the secondary is truncated, and further characterized by some or all of the portions of the stepped flow-line optic which follow the flow lines being absent, leaving only those portions which cross the flow lines, that is, the heliostats, and in which the continuous portions that may exist (not stepped) of the primary concentrator are also divided into heliostats; or an optical system with primary concentrator of the Fresnel type and adjacent secondary concentrator, the secondary receiver set being above the primary, and characterized by the primary concentrator containing a stepped flow-line optic which shape verifies the condition that it reflects a set of edge rays so as to make them tangent to the receiver and the other set of edge rays in the direction of the secondary concentrator, which shape verifies the condition that it, on its turn, reflects the edge rays it receives from the primary concentrator in directions tangent to the receiver, producing there, theoretically, a maximum concentration, and in which the secondary is truncated, and further characterized by the heliostats being able to rotate around themselves to follow the apparent daily motion of the sun; thus forming a concentrator with multiple receivers.
 17. The optical system of claim 16, characterized by the heliostats being placed on a wave shaped surface, with cylindrical geometry, corresponding, basically, to a curve that optically conserves etendue.
 18. The optical system of claim 16, characterized by the heliostats of the primary concentrator being flat or curved.
 19. The optical system of claim 6, characterized by the overall shape of the primary concentrator being flat.
 20. The optical system of claim 16, characterized by the receivers having a larger size than that they would have if dimensioned for maximum or ideal concentration.
 21. The optical system of claim 16, characterized by comprising transparent covers substantially perpendicular to the flow lines and mirrors (mirrored on both sides) which substantially follow the flow lines for convection reduction next to the receiver.
 22. A method of concentrating solar energy, said method comprising: concentrating solar energy using an optical system with primary concentrator of the Fresnel type and adjacent secondary concentrator, the secondary receiver set being above the primary, and characterized by the primary concentrator containing a stepped flow-line optic which shape verifies the condition that it reflects a set of edge rays so as to make them tangent to the receiver and the other set of edge rays in the direction of the secondary concentrator, which shape verifies the condition that it, on its turn, reflects the edge rays it receives from the primary concentrator in directions tangent to the receiver, producing there, theoretically, a maximum concentration, and in which the secondary is truncated. 